Two-dimensional solute transport in finite homogeneous porous formations

An analytical approach to two-dimensional non-reactive solute transport in finite homogeneous porous formations is compared with the numerical result obtained from two-level explicit finite difference method. The analytical solution is derived with time-dependent point-source contamination expressed as logistic sigmoid functions for three different types of velocity expressions. First, the flow velocity in the aquifer is asymptotic in nature, second, the flow velocity is an exponentially decreasing function and third the flow velocity is sigmoid expression. These velocity expressions represent the groundwater flow in complex nature of geological formation. The geological formation is initially polluted. This may be represented by a mathematical expression i.e., exponentially decreasing function of space. A particular case is derived which validates the solution, and the analytical solution is illustrated using suitable input parameters.